What is the sine value of an angle of $frac{pi}{4}$ radians on the unit circle?
Answer 1
Daniel Carter
To find the sine value of an angle of $\frac{\pi}{4}$ radians on the unit circle, we use the unit circle properties. The angle $\frac{\pi}{4}$ radians is equivalent to 45 degrees.
On the unit circle, the coordinates of the point at $\frac{\pi}{4}$ radians are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$. The sine of the angle is the y-coordinate of this point.
Therefore, $\sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$.
Answer 2
Emma Johnson
First, recall that the unit circle is a circle of radius 1 centered at the origin. The angle $frac{pi}{4}$ radians corresponds to 45 degrees.
The sine function gives the y-coordinate of the point on the unit circle at the given angle. At $frac{pi}{4}$ radians, the coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus, the sine of $frac{pi}{4}$ is the y-coordinate, which is $frac{sqrt{2}}{2}$.
Answer 3
Maria Rodriguez
To determine $sin left( frac{pi}{4}
ight)$, we find the y-coordinate of the point on the unit circle at that angle.
From the unit circle, the coordinates at $frac{pi}{4}$ are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
So, $sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$.
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